The Zermelo conditions and higher order homogeneous functions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216275%3A25530%2F13%3A39892863" target="_blank" >RIV/00216275:25530/13:39892863 - isvavai.cz</a>

Alternative codes found

RIV/61988987:17310/13:A1401A5E

Result on the web

<a href="http://dx.doi.org/10.5486/PMD.2013.5265" target="_blank" >http://dx.doi.org/10.5486/PMD.2013.5265</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5486/PMD.2013.5265" target="_blank" >10.5486/PMD.2013.5265</a>

Result language

angličtina

Original language name

The Zermelo conditions and higher order homogeneous functions

Original language description

Invariance under reparametrizations of integral curves of higher order differential equations, including variational equations related to Finsler geometry, is studied. The classical homogeneity concepts are introduced within the theory of (jet) differential groups, known in the theory of differential invariants. On this basis the well-known generalizations of the Euler theorem are obtained (the Zermelo conditions). It is shown that every integral curve of a system of differential equations whose left-hand sides are higher order positive homogeneous functions, is invariant with respect to all reparametrizations, i.e. a set solution. Then the positive homogeneity concept is applied to second order variational equations. We show that the systems with positive homogeneous Lagrangians are defined by positive homogeneous functions, and vice versa.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2013

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Publicationes Mathematicae

ISSN

0033-3883

e-ISSN

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Volume of the periodical

82

Issue of the periodical within the volume

1

Country of publishing house

HU - HUNGARY

Number of pages

18

Pages from-to

59-76

UT code for WoS article

000324896500006

EID of the result in the Scopus database

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